The sum of two angles is $92^\circ$. Angle 2 is $49^\circ$ smaller than $2$ times angle 1. What are the measures of the two angles in degrees?
Solution: Let $x$ equal the measure of angle 1 and $y$ equal the measure of angle 2. The system of equations is then: ${x+y = 92}$ ${y = 2x-49}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${2x-49}$ for $y$ in the first equation. ${x + }{(2x-49)}{= 92}$ Simplify and solve for $x$ $ x+2x - 49 = 92 $ $ 3x-49 = 92 $ $ 3x = 141 $ $ x = \dfrac{141}{3} $ ${x = 47}$ Now that you know ${x = 47}$ , plug it back into $ {y = 2x-49}$ to find $y$ ${y = 2}{(47)}{ - 49}$ $y = 94 - 49$ ${y = 45}$ You can also plug ${x = 47}$ into $ {x+y = 92}$ and get the same answer for $y$ ${(47)}{ + y = 92}$ ${y = 45}$ The measure of angle 1 is $47^\circ$ and the measure of angle 2 is $45^\circ$.